Fermi-surface evolution across the magnetic phase transition in the Kondo lattice model

We derive, by means of an extended Gutzwiller wave function and within the Gutzwiller approximation, the phase diagram of the Kondo lattice model. We find that generically, namely, in the absence of nesting, the model displays an $f$-electron Mott localization accompanied by a discontinuous change of the conduction-electron Fermi surface as well as by magnetism. When the noninteracting Fermi surface is close to nesting, the Mott localization disentangles from the onset of magnetism. First the paramagnetic heavy-fermion metal turns continuously into an itinerant magnet—the Fermi surface evolves smoothly across the transition—and afterward Mott localization intervenes with a discontinuous rearrangement of the Fermi surface. We find that the $f$-electron localization remains even if magnetism is prevented and is still accompanied by a sharp transfer of spectral weight at the Fermi energy within the Brillouin zone. We further show that the Mott localization can be also induced by an external magnetic field, in which case it occurs concomitantly with a metamagnetic transition.

Figure 1

(Color online) Variational phase diagram as a function of the conduction electron density $n_c$ and of the Kondo exchange in units of half the bandwidth, $J/D$. The solid line with the circles represents a first-order line, while the dotted line is a second-order transition. The error bars along the second-order phase-transition line reflect the variational uncertainty of a precise location of the continuous transition. The same problem does not arise along the discontinuous first-order line. PM stands for paramagnetic heavy-fermion metal, while AF stands for an itinerant antiferromagnet; the subscripts “$e$” and “$h$” are borrowed from Ref. 21 and refer to the electronlike $\left(e\right)$ or holelike $\left(h\right)$ character of the Fermi surface, see Fig. 3.

Figure 2

(Color online) The magnetic order parameter as a function of $J/D$ for $n_c=0.92$ (left panel) and 0.7 (right panel). Notice that for $n_c=0.92$ the order parameter grows continuously below a critical $J/D\simeq 0.6$—second-order phase transition—until at $J/D\simeq 0.36$ it jumps abruptly—first-order transition. For $n_c=0.7$ only a first-order transition with a jump from zero to a finite value of the order parameter is observed.

Figure 3

(Color online) The conduction-electron spectral function at the chemical potential for a two-dimensional square lattice. Panels (a), (b), and (c) show the evolution of the spectral function $A\left(\mathbf{k}\right)$ at the chemical potential for $n_c=0.92$ in the paramagnetic phase (a) with $J/D=0.8$, right after the second-order transition, (b) with $J/D=0.4$, and finally below the first-order transition (c) with $J/D=0.16$. Panels (d) and (e) show the same evolution with $n_c=0.7$ where there is only the first-order transition.

Figure 4

(Color online) Evolution of the band structure within the magnetic Brillouin zone of the optimized variational Hamiltonian (13) for $n_c=0.92$ as a function of $J/D$ and across the first-order transition. Left panel: $J/D=0.2$; right one: $J/D=0.36$.

Figure 5

(Color online) One-dimensional representation of the different variational band structures in the two magnetic phases close to $n_c=1$ drawn in the magnetic Brillouin zone. Small $J/D$ phase: (a) represents nonhybridized $c$ and $f$ bands split by antiferromagnetism; and (b) what happens once a small hybridization is switched on. Large $J/D$ phase: (c) represents nonmagnetic hybridized $c$ and $f$ bands in the folded Brillouin zone; and (d) what happens once a small antiferromagnetic order parameter is switched on.

Figure 6

(Color online) Variational energy as a function of $J/D$ at $n_c=0.8$ in the paramagnetic sector. A kink is visible at $J/D\simeq 0.21$. We note the finite curvature of the energy at low $J/D$, which, as we checked, is compatible with second-order perturbation theory.

Figure 7

(Color online) Spectral function at the chemical potential for $n_c=0.8$ and $J/D$ (a) above and (b) below the critical value.

Figure 8

(Color online) Behavior of the average Kondo exchange, $K/D$, and hopping, $T/D$ (in units of $D$, half the conduction bandwidth).

Figure 9

(Color online) Evolution of the uniform magnetization as a function of an external magnetic field applied in the paramagnetic phase ($J/D=0.45$ at $n_c=0.88$). Insets show the spectral functions for the majority (top panel) and minority (bottom panel) spins across the metamagnetic transition.